Effect of turbulent kinetic helicity on diffusive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math> effect for large scale dynamo

We investigated a plasma system with kinematic viscosity $\ensuremath{\nu}=0.006$ and magnetic diffusivity $\ensuremath{\eta}=0.006$, driven by helical kinetic energy, to study the dynamics of energy and helicity in magnetic diffusion. Using the numerical data obtained, we explored methods to determine the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ coefficients that linearize the nonlinear electromotive force and the dynamo process. Initially, we applied conventional statistical approaches such as mean field theory, direct interaction approximation, and eddy-damped quasinormal Markovian closure. We then proposed a simpler alternative method using large scale magnetic data and turbulent kinetic data to calculate $\ensuremath{\alpha}$ and $\ensuremath{\beta}$. Our findings show that, while $\ensuremath{\alpha}$ qualitatively aligns with theoretical predictions, $\ensuremath{\beta}$ remains negative, indicating an inverse cascade of energy through magnetic diffusion. This deviates from conventional models and was further analyzed using a recursive method in the second moment identity, revealing that small scale kinetic helicity couples with large scale current density to transport energy inversely. We validated our method by reproducing the numerically calculated data. The consistency between our method and direct numerical simulations suggests that the negative diffusion process in plasma has a physical basis.